1. Field of the Invention
The invention regards a method for co-ordinating and synchronising the movement of servo-assisted axes intended for realising a certain application in various sectors of industry, such as:                flying cuts and interpolation jobs, both linear and circular, on plastic, metal sheet and cardboard;        product packaging;        winding of cable, metallic wire, strap, etc., with strand-guiding functions;        layering of fabrics or pastry with folding machines, mainly used in the textile and food industry;        silk-screen or flexographic printing with circular plates.        
2. Description of Related Art
It is known that in the realisation of operating machines, in particular industrial ones which are automatic controlled by PLCs (Programmable Logic Controllers) or by a PC (personal computer), the need to co-ordinate and synchronise the movement of many servo-assisted axes belonging to the same machine crops up ever more frequently.
The electronic controls to satisfy the aforementioned requirement use specific commands, collected in a movement program which is executed in sequence, with which both the type of “trajectory”—understood to mean the function which links the displacements of two or more axes to each other in space—and the “law of motion” of the axes themselves—understood to mean the function which describes the progression of space in time relative to the displacement of each axis.
The “transfer function” of the law of motion is the result of two fundamental magnitudes in the movement of the axes: speed and acceleration. By analysing the progression of space in time and by carrying out first and second derivative operations the speed and acceleration can be worked out as a function of time. In a program for moving many axes some fundamental parameters (speed and acceleration) have to be defined for each axis, upon the basis of which the specific laws of motion for each individual axis shall be calculated, said laws, applied simultaneously, going on to produce the desired trajectories in space.
There are two main systems existing on the market for the description and consequent execution of trajectories for executing the co-ordinating and synchronising functions of axes.
The first system is generally known as “numeric controls” and is based upon the principle of the decomposition of complex trajectories, usually described under the form of polynomial or trigonometric functions, in three types of elementary trajectories, which are:                1. point-to-point trajectories;        2. trajectories by linear interpolation;        3. trajectories by circular interpolation.        
A complex trajectory is thus carried out as a succession of elementary trajectories. If the elementary trajectories are then combined with each other to be applied simultaneously on many axes complex interpolations are obtained such as tangential, helical and spherical ones.
The “numeric controls” just described require a high processing capacity which is commonly executed by sophisticated processors, such as personal computers, with the help of specific software packages. The use thereof is usually foreseen in the cases of treatments with a medium-high complexity.
The second method in use for coordinating and moving servo-assisted axes is known as “CAMMING” and is based upon the decomposition of the global motion of each individual axis into elementary movements, each related solely to the motion of a first axis, called the reference “MASTER axis” which is common to all the other axes, called “SLAVE axes”.
The MASTER axis can be either a real axis or a virtual axis, that is a mathematical algorithm which simulates the ideal behaviour of an axis which executes a point-to-point trajectory. The trajectory of the MASTER axis is decomposed into a finite number of elements, where each element can be described as an absolute or incremental co-ordinate, and with each element is associated the corresponding absolute co-ordinate of every single SLAVE axis.
In practice, if the absolute positions of the MASTER axis are represented as x-coordinates of a Cartesian x/y plane and the corresponding absolute positions of the SLAVE axis relative to the same instant considered are represented as y-coordinates, a succession of points which can be connected together which describe a trajectory which is commonly referred to as “cam” is obtained. The succession of points thus obtained is put into a table, known as “CAM TABLE”, which thus contains an association between the absolute position which each of the axes to be controlled, i.e. every single SLAVE axis, must take up, for every position of the MASTER axis.
In mathematical terms, calling the spatial coordinate of the SLAVE Qs and the spatial coordinate of the MASTER Qm, the “CAM TABLE” describes the function Qs=f(Qm). During the execution of the movement, the position of the MASTER directly determines the position of the SLAVE; consequently, the variations in time of the position of the MASTER determine the corresponding variations of the individual SLAVES, and thus the dynamic progression thereof.
Still expressing the concept in mathematical terms, calling the time function describing the motion of the MASTER Qm(t), the function of the motion of the SLAVE is determined by the function Qs(t)=f(Qm(t)).
Each line of the aforementioned “CAM TABLE”, also known as cam “sector”, is calculated using a personal computer with suitable software programs according to the “geometry” of the cams and their dynamic progression. The same programs allow, moreover, to simulate and visualise the laws of motion.
Once calculated, the “CAM TABLE” is “downloaded” into the electronic device which manages the moving.
The advantage given by the CAMMING technique with respect to a “numeric control” is in the simplification of the calculation required of the electronic device which executes the trajectories of the single axes, the table being the result of processing executed beforehand.
This same technique—which in any case represents a substantial simplification with respect to a “numeric control”—nevertheless has big drawbacks in its application.
A first drawback is given by the fact that the calculations necessary for quickly completing the points of a “CAM TABLE”, taking into account the maximum accelerations and decelerations allowed of the SLAVE axis, are rather complex and require the systematic use of a personal computer.
A further drawback consists of the fact that the “CAM TABLE” completed on the basis of complex calculations cannot be varied “on the spot” in the electronic devices which manage the moving. To allow variations many tables are usually calculated, which can however only be switched with each other in a few determined positions of the MASTER axis. The use of multiple tables, besides requiring greater memory in the electronic device, does not at all eliminate the drawback of rigidity in the CAMMING technique applied to the control of axes.
With the invention in object it is intended to obtain, as an alternative to conventional CAMMING, a system for controlling axes, whilst still guaranteeing the simplicity of processing by electronic devices which manage the moving, overcomes the aforementioned limits and drawbacks.
A first purpose of the method according to the invention is that of being able to evaluate the dynamic behaviour of servo-assisted axes without making use of special SOFTWARE programs on a personal computer, which, as stated above, require the entry of a large amount of data and, moreover, are not always available on line during treatment.
Another purpose of the same method is to allow laws of motion to be applied to the controlled axes according to mathematical functions of various types, such as linear, trigonometric or special.
A further purpose of the method is to allow the manipulation on the spot of the calculations, both of the MASTER axis and of the SLAVE axes.
Yet another purpose of the method is to allow the execution of unconditioned jumps in different positions inside the same described trajectories.